SPS SPS FM Pure 2022 February — Question 9

Exam BoardSPS
ModuleSPS FM Pure (SPS FM Pure)
Year2022
SessionFebruary
TopicRoots of polynomials

9. The equation \(4 x ^ { 4 } - 4 x ^ { 3 } + p x ^ { 2 } + q x - 9 = 0\), where \(p\) and \(q\) are constants, has roots \(\alpha , - \alpha , \beta\) and \(\frac { 1 } { \beta }\).
  1. Determine the exact roots of the equation.
  2. Determine the values of \(p\) and \(q\).
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